WASHINGTON (AP), May 13 - Republican Mitt Romney faces a deeply unpleasant choice in his all-but-announced bid for the White House. He signaled Thursday that he'd rather be charged with inspiring President Barack Obama's health care overhaul than with switching positions on a fourth big issue that's vital to conservative voters.

Either accusation, if it sticks, might deny him the GOP nomination. Conservatives despise Obama's 2010 health care law, especially the requirement that everyone obtain medical insurance. That same requirement is a cornerstone of the 2006 Massachusetts law that Romney championed as governor. Many advisers have urged Romney to apologize, say he made a big mistake and move on.

But voters of almost every stripe dislike political flip-floppers. And that puts Romney in a different jam.

As he shifted from Massachusetts governor to a Republican presidential hopeful, he reversed his stands on abortion laws, gay rights and gun laws. Flipping on a fourth big issue might undo him.

So Romney has decided to stick with a sometimes confusing, legalistic defense of the ground-breaking health law he enacted in Massachusetts. In a 29-minute talk and slide show Thursday in Michigan, he tried to make a political virtue of his campaign necessity.

``A lot of pundits around the nation are saying that I should just stand up and say this whole thing was a mistake, that it was just a bone-headed idea and I should just admit it,'' Romney told a room of college Republicans. ``There's only one problem with that: It wouldn't be honest. I, in fact, did what I believe was right for the people of my state.''

There's the rub for Romney. If mandated insurance coverage was right for the state he governed, how can it be so terribly wrong for the nation Obama oversees?

Romney said Massachusetts' health care system differed from those in Montana, Mississippi and elsewhere. Yet he described a commonplace problem: People realized they could receive free emergency medical care without buying health insurance, forcing others to pick up the tab.

``This was what we call the free-rider problem,'' he said. ``It wasn't a large number, but a growing number.''

Through taxes or higher medical fees, other state residents were unfairly forced to subsidize these free riders, Romney said. So the state enacted a law ``that said either have insurance, or we're going to charge you'' a fair share. The charge wasn't huge, he said, but enough to be ``a pretty big incentive to encourage people to get insured.''

That's a justification that Obama and congressional Democrats also used for passing the 2010 law that, when fully phased in, will require everyone to have health coverage. Romney touched on the other chief reason as well. Universal coverage can be used to bar insurers from turning away people with ``pre-existing conditions,'' because patients no longer can wait until they are seriously ill to buy insurance.

Romney portrayed Massachusetts' problems as almost unique. ``Our plan was a state solution to a state problem,'' he said. Obama's program, he said, ``is a power grab by the federal government to put in place a one-size-fits-all plan across the nation.''

But Romney himself noted that it is ``actually true in most states'' that people receive free treatment in emergency rooms.

Analysts and political strategists were skeptical.

``Romney trotted out the federalism argument once again, calling Obamacare a `power grab,''' wrote Jennifer Rubin, a conservative blogger at The Washington Post. ``But conservatives for nearly two years have been arguing that NO government should require individuals to purchase something they don't want.''

Former Sen. Rick Santorum, who also is seeking the GOP presidential nomination, criticized Romney for trying ``to institute the precursor to national socialized medicine.''

Even some of Romney's closest friends seem unmoved. Sen. Jim DeMint, R-S.C., said Romney ``had admirable goals of making private health insurance more affordable, but the Massachusetts plan didn't work.''

DeMint had a kinder tone two months ago. He told The Hill newspaper: ``One of the reasons I endorsed Romney (in 2008) is his attempts to make private health insurance available at affordable prices. ... He started with some good ideas that were essentially hijacked by the Democrat legislature.''

Before Romney spoke on Thursday, The Wall Street Journal's editorial page - it is influential with many conservatives- wrote that ``if he does not change his message'' on the Massachusetts health law, ``he might as well try to knock off Joe Biden and get on the Obama ticket.''

But changing his message would invite renewed charges that Romney lacks convictions and authenticity.

In his successful 2002 gubernatorial race, and his unsuccessful 1994 bid to unseat liberal Sen. Edward M. Kennedy, D-Mass., Romney took stands he since has renounced. Abortion should be safe and legal, he said at the time, and he vowed to be a stronger advocate for gay rights than was Kennedy. He supported gun control measures and distanced himself from Ronald Reagan.

Romney says he changed his views on those topics after periods of serious re-examination. Still, they leave him open to attacks.

``The big problem for Mitt Romney is he has a conviction problem,'' said Neera Tanden, a top adviser to President Bill Clinton and to his wife, Hillary Rodham Clinton, when she was a senator and a presidential candidate. Romney's resume is strong, Tanden said, ``but voters don't know what he stands for.''

Turning his back on his landmark Massachusetts health law would exacerbate that problem. Romney said Thursday he is standing by the Massachusetts law ``despite the fact it's gone from being seen as an asset to being seen as a liability politically.''

Romney has picked his battle. The outcome may determine whether he is the Republican who will challenge Obama next year.